To find the area of the rectangle within the composite shape, we need to first calculate the area of the two congruent right triangles.
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Area of one triangle: The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base is 3 inches and the height is 4 inches, so: \[ \text{Area} = \frac{1}{2} \times 3 \times 4 = \frac{12}{2} = 6 \text{ square inches} \]
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Area of two triangles: Since there are two congruent triangles, we multiply the area of one triangle by 2: \[ \text{Total Area of Triangles} = 2 \times 6 = 12 \text{ square inches} \]
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Area of the rectangle: The total area of the composite figure is given as 40 square inches. To find the area of the rectangle, we subtract the area of the triangles from the total area: \[ \text{Area of Rectangle} = \text{Total Area} - \text{Total Area of Triangles} \] \[ \text{Area of Rectangle} = 40 - 12 = 28 \text{ square inches} \]
Thus, the area of the rectangle within the composite shape is 28 square inches.